2012/03/23 by Fábio José Bertoloto, Bertoloto, Fábio José
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #math.FA #msc:30H10 #msc:46G10 #msc:46G20
paper · pdf · doi:10.48550/arxiv.1203.5322
arxiv created 2012/03/23 · arxiv updated 2012/03/26
In this work we study the vector-valued Hardy spaces H p (D; F) (1 ≤ p ≤ ∞) and their relationship with RNP, ARNP and the UMDP properties. By following the approach of Taylor in the scalar-valued case, we prove that, when F and F have the ARNP property, then H p (D; F) and H q (D; F) are canonically topologically isomorphic (for p, q ∈ (1, ∞) conjugate indices) if and only if F has the UMDP.